Question

HELP?!?!
Solve using linear combination.

1. 2x+7y=5
3x-y=(-4)

2. 2x+5y=(-1)
3x-2y=8

3. 3x+y=(-12)
(-2x)+y=8

Answer 1

By "using linear combination", I'm assuming your instructor wants you to solve by elimination. It helps to write out each set of equations such that the x terms are on top of one another and the y terms are on top of one another.
I'll walk you through problem 1:
\[\begin{array}{lcl} 2x + 7y & = & 5 \\ 3x - y & = & -4 \end{array}\]
You want to multiple the first equation by some number and the second equation by some different number such that when you add (or subtract) both equations, either the x- or y-terms drop out from the resulting equation. Say I want to eliminate the x-term. If I multiply the first equation by -3 and the second equation by 2, I get
\[\begin{array}{rcl} -3(2x + 7y) & = & -3(5) \\ 2(3x - y) & = & 2(-4) \end{array}\]
Which then changes the two equations into
\[\begin{array}{cl} -6x - 21y & = & -15 \\ 6x - 2y & = & -8 \end{array}\]
Now if we add the two equations, notice that the x terms drop out (remember that -6 + 6 = 0).
\[-23y = -23\]
We can then solve for y and we see that
\[\frac{-23y}{-23} = \frac{-23}{-23} \]
so \[y = 1\]
Now plug that result (what y is equal to) into any of the two equations in problem 1 in order to solve for x. Using the first equation,
\[2x + 7y = 5\]
\[2x + 7(1) = 5\]
\[2x + 7 = 5\]
\[2x = -2\]
\[\frac{2x}{2} = \frac{-2}{2}\]
\[x = -1\]

Answer 2

Thank you